论文标题
使用任意局部对称性设计本地最大纠缠的量子状态
Designing locally maximally entangled quantum states with arbitrary local symmetries
论文作者
论文摘要
量子信息中许多LOCC协议的关键要素之一是具有局部对称性的多片（本地）最大纠缠的量子状态，也就是临界状态。我们展示了如何使用任意大型局部统一对称性设计关键状态。我们解释说，这些状态可以在具有有限数量模式的玻色子或费米子的可区分陷阱的量子系统中实现。然后，设计的量子状态的局部对称性等于在所有陷阱上对角线作用的统一局部模式操作。因此，这样的对称性自然受到保护，免受模式运算符物理实现中发生的错误。我们还将结果与具有特定渐近对角线对称性的所谓严格半固定状态联系起来。我们的主要技术结果指出，$ \ mathrm {su}（n）$的任何不可约表示的$ n $ th张量均包含琐碎表示的副本。这是通过利用我们称为望远镜的某些组合对象的Littlewood-Richardson规则进行直接组合分析来建立的。
One of the key ingredients of many LOCC protocols in quantum information is a multiparticle (locally) maximally entangled quantum state, aka a critical state, that possesses local symmetries. We show how to design critical states with arbitrarily large local unitary symmetry. We explain that such states can be realised in a quantum system of distinguishable traps with bosons or fermions occupying a finite number of modes. Then, local symmetries of the designed quantum state are equal to the unitary group of local mode operations acting diagonally on all traps. Therefore, such a group of symmetries is naturally protected against errors that occur in a physical realisation of mode operators. We also link our results with the existence of so-called strictly semistable states with particular asymptotic diagonal symmetries. Our main technical result states that the $N$th tensor power of any irreducible representation of $\mathrm{SU}(N)$ contains a copy of the trivial representation. This is established via a direct combinatorial analysis of Littlewood-Richardson rules utilising certain combinatorial objects which we call telescopes.
